Is it common for girl to date guys that are not their type (looks)?

We all know girls care about looks, just as much if not more than guys. And everyone has a "type" look wise based on hair, eyes, height, weight, build etc.

My question is, how strict are girls to their decided type? Are they dead set on that being what they want and will never look outside it? Or if they meet someone who they like as a person, will they be ok with him not being their "type" physically?